Mugabe said Sunday the violence was a blight on the country, Radio France Internationale reported.
"The leadership of the inclusive government urges you to desist from any acts of violence that will cause harm to others and become a blight on our society," Mugabe said during a speech at the National Sports Stadium in Harare. "We need to foster an environment of tolerance and treating each other with dignity and respect irrespective of age, gender, race, ethnicity, tribe, political or religious affiliation."
For only the second time, the opposition Movement for Democratic Change was included in independence celebrations, Radio France Internationale reported.
Mugabe was sworn in as president after bitter, violent elections in 2008. MDC leader Morgan Tsvangirai was named prime minister following protracted negotiations to establish a system of shared governance.
Mugabe, 86, led Zimbabwe to independence in 1980.